options(warn=-1)
library(pacman)
p_load(dplyr)
source('../lib/import.R')
#
# Es una librería de funciones comunes desarrolladas a partir de este TP.
import('../lib/common-lib.R')
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## ---
## biotools version 4.1
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# Funciones especificas para este TP.
import('../scripts/helper_functions.R')
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set.seed(1)

1. Cargamos el dataset

1.1. Cargamos el dataset nasa-asteroids y excluirnos observaciones con valores faltaste.

dataset <- loadcsv('../datasets/nasa.csv')
str(dataset)
## 'data.frame':    4687 obs. of  40 variables:
##  $ Neo.Reference.ID            : int  3703080 3723955 2446862 3092506 3514799 3671135 2495323 2153315 2162463 2306383 ...
##  $ Name                        : int  3703080 3723955 2446862 3092506 3514799 3671135 2495323 2153315 2162463 2306383 ...
##  $ Absolute.Magnitude          : num  21.6 21.3 20.3 27.4 21.6 19.6 19.6 19.2 17.8 21.5 ...
##  $ Est.Dia.in.KM.min.          : num  0.1272 0.1461 0.2315 0.0088 0.1272 ...
##  $ Est.Dia.in.KM.max.          : num  0.2845 0.3266 0.5177 0.0197 0.2845 ...
##  $ Est.Dia.in.M.min.           : num  127.2 146.1 231.5 8.8 127.2 ...
##  $ Est.Dia.in.M.max.           : num  284.5 326.6 517.7 19.7 284.5 ...
##  $ Est.Dia.in.Miles.min.       : num  0.07905 0.09076 0.14385 0.00547 0.07905 ...
##  $ Est.Dia.in.Miles.max.       : num  0.1768 0.203 0.3217 0.0122 0.1768 ...
##  $ Est.Dia.in.Feet.min.        : num  417.4 479.2 759.5 28.9 417.4 ...
##  $ Est.Dia.in.Feet.max.        : num  933.3 1071.6 1698.3 64.6 933.3 ...
##  $ Close.Approach.Date         : chr  "1995-01-01" "1995-01-01" "1995-01-08" "1995-01-15" ...
##  $ Epoch.Date.Close.Approach   : num  7.89e+11 7.89e+11 7.90e+11 7.90e+11 7.90e+11 ...
##  $ Relative.Velocity.km.per.sec: num  6.12 18.11 7.59 11.17 9.84 ...
##  $ Relative.Velocity.km.per.hr : num  22017 65210 27327 40226 35427 ...
##  $ Miles.per.hour              : num  13681 40519 16980 24995 22013 ...
##  $ Miss.Dist..Astronomical.    : num  0.419 0.383 0.051 0.285 0.408 ...
##  $ Miss.Dist..lunar.           : num  163.2 149 19.8 111 158.6 ...
##  $ Miss.Dist..kilometers.      : num  62753692 57298148 7622912 42683616 61010824 ...
##  $ Miss.Dist..miles.           : num  38993336 35603420 4736658 26522368 37910368 ...
##  $ Orbiting.Body               : chr  "Earth" "Earth" "Earth" "Earth" ...
##  $ Orbit.ID                    : int  17 21 22 7 25 40 43 22 100 30 ...
##  $ Orbit.Determination.Date    : chr  "2017-04-06 08:36:37" "2017-04-06 08:32:49" "2017-04-06 09:20:19" "2017-04-06 09:15:49" ...
##  $ Orbit.Uncertainity          : int  5 3 0 6 1 1 1 0 0 0 ...
##  $ Minimum.Orbit.Intersection  : num  0.02528 0.18693 0.04306 0.00551 0.0348 ...
##  $ Jupiter.Tisserand.Invariant : num  4.63 5.46 4.56 5.09 5.15 ...
##  $ Epoch.Osculation            : num  2458000 2458000 2458000 2458000 2458000 ...
##  $ Eccentricity                : num  0.426 0.352 0.348 0.217 0.21 ...
##  $ Semi.Major.Axis             : num  1.41 1.11 1.46 1.26 1.23 ...
##  $ Inclination                 : num  6.03 28.41 4.24 7.91 16.79 ...
##  $ Asc.Node.Longitude          : num  314.4 136.7 259.5 57.2 84.6 ...
##  $ Orbital.Period              : num  610 426 644 514 496 ...
##  $ Perihelion.Distance         : num  0.808 0.718 0.951 0.984 0.968 ...
##  $ Perihelion.Arg              : num  57.3 313.1 248.4 18.7 158.3 ...
##  $ Aphelion.Dist               : num  2.01 1.5 1.97 1.53 1.48 ...
##  $ Perihelion.Time             : num  2458162 2457795 2458120 2457902 2457814 ...
##  $ Mean.Anomaly                : num  264.8 173.7 292.9 68.7 135.1 ...
##  $ Mean.Motion                 : num  0.591 0.845 0.559 0.7 0.726 ...
##  $ Equinox                     : chr  "J2000" "J2000" "J2000" "J2000" ...
##  $ Hazardous                   : chr  "True" "False" "True" "False" ...

1.2. Las siguientes columnas las excluimos ya sea por que son no numerica, o colineales con las columna que si son parte de nuestro analisis.

excluded_columns <- c(
  'Neo.Reference.ID',
  'Name',
  'Close.Approach.Date',
  'Epoch.Date.Close.Approach',
  'Orbit.ID',
  'Orbit.Determination.Date',
  'Orbiting.Body',
  'Est.Dia.in.Feet.min.',
  'Est.Dia.in.Feet.max.',
  'Est.Dia.in.M.min.',
  'Est.Dia.in.M.max.',
  'Est.Dia.in.KM.min.',
  'Est.Dia.in.KM.max.',
  'Equinox',
  'Orbit.Uncertainity'
)

ds_step_1 <- dataset %>% dplyr::select(-excluded_columns) %>% na.omit
## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(excluded_columns)` instead of `excluded_columns` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
rm(dataset)

str(ds_step_1)
## 'data.frame':    4687 obs. of  25 variables:
##  $ Absolute.Magnitude          : num  21.6 21.3 20.3 27.4 21.6 19.6 19.6 19.2 17.8 21.5 ...
##  $ Est.Dia.in.Miles.min.       : num  0.07905 0.09076 0.14385 0.00547 0.07905 ...
##  $ Est.Dia.in.Miles.max.       : num  0.1768 0.203 0.3217 0.0122 0.1768 ...
##  $ Relative.Velocity.km.per.sec: num  6.12 18.11 7.59 11.17 9.84 ...
##  $ Relative.Velocity.km.per.hr : num  22017 65210 27327 40226 35427 ...
##  $ Miles.per.hour              : num  13681 40519 16980 24995 22013 ...
##  $ Miss.Dist..Astronomical.    : num  0.419 0.383 0.051 0.285 0.408 ...
##  $ Miss.Dist..lunar.           : num  163.2 149 19.8 111 158.6 ...
##  $ Miss.Dist..kilometers.      : num  62753692 57298148 7622912 42683616 61010824 ...
##  $ Miss.Dist..miles.           : num  38993336 35603420 4736658 26522368 37910368 ...
##  $ Minimum.Orbit.Intersection  : num  0.02528 0.18693 0.04306 0.00551 0.0348 ...
##  $ Jupiter.Tisserand.Invariant : num  4.63 5.46 4.56 5.09 5.15 ...
##  $ Epoch.Osculation            : num  2458000 2458000 2458000 2458000 2458000 ...
##  $ Eccentricity                : num  0.426 0.352 0.348 0.217 0.21 ...
##  $ Semi.Major.Axis             : num  1.41 1.11 1.46 1.26 1.23 ...
##  $ Inclination                 : num  6.03 28.41 4.24 7.91 16.79 ...
##  $ Asc.Node.Longitude          : num  314.4 136.7 259.5 57.2 84.6 ...
##  $ Orbital.Period              : num  610 426 644 514 496 ...
##  $ Perihelion.Distance         : num  0.808 0.718 0.951 0.984 0.968 ...
##  $ Perihelion.Arg              : num  57.3 313.1 248.4 18.7 158.3 ...
##  $ Aphelion.Dist               : num  2.01 1.5 1.97 1.53 1.48 ...
##  $ Perihelion.Time             : num  2458162 2457795 2458120 2457902 2457814 ...
##  $ Mean.Anomaly                : num  264.8 173.7 292.9 68.7 135.1 ...
##  $ Mean.Motion                 : num  0.591 0.845 0.559 0.7 0.726 ...
##  $ Hazardous                   : chr  "True" "False" "True" "False" ...

2. Eliminamos las columnas que están altamente co-relacionadas

Excluimos las columnas que tienen un correlación mayor al 80%. Del grupo altamenten correlacionesdos nos quedamos con una sola variable ya que todas con muy simialres.

high_correlated_columns <- find_high_correlated_columns(
  feat(ds_step_1), 
  cutoff=0.8
)

print(high_correlated_columns)
##  [1] "Aphelion.Dist"                "Miss.Dist..kilometers."      
##  [3] "Miss.Dist..Astronomical."     "Miss.Dist..miles."           
##  [5] "Jupiter.Tisserand.Invariant"  "Semi.Major.Axis"             
##  [7] "Relative.Velocity.km.per.sec" "Relative.Velocity.km.per.hr" 
##  [9] "Orbital.Period"               "Est.Dia.in.Miles.max."       
## [11] "Epoch.Osculation"
ds_step_2 <- ds_step_1 %>% dplyr::select(-high_correlated_columns[-1])

rm(ds_step_1)
str(ds_step_2)
## 'data.frame':    4687 obs. of  15 variables:
##  $ Absolute.Magnitude        : num  21.6 21.3 20.3 27.4 21.6 19.6 19.6 19.2 17.8 21.5 ...
##  $ Est.Dia.in.Miles.min.     : num  0.07905 0.09076 0.14385 0.00547 0.07905 ...
##  $ Miles.per.hour            : num  13681 40519 16980 24995 22013 ...
##  $ Miss.Dist..lunar.         : num  163.2 149 19.8 111 158.6 ...
##  $ Minimum.Orbit.Intersection: num  0.02528 0.18693 0.04306 0.00551 0.0348 ...
##  $ Eccentricity              : num  0.426 0.352 0.348 0.217 0.21 ...
##  $ Inclination               : num  6.03 28.41 4.24 7.91 16.79 ...
##  $ Asc.Node.Longitude        : num  314.4 136.7 259.5 57.2 84.6 ...
##  $ Perihelion.Distance       : num  0.808 0.718 0.951 0.984 0.968 ...
##  $ Perihelion.Arg            : num  57.3 313.1 248.4 18.7 158.3 ...
##  $ Aphelion.Dist             : num  2.01 1.5 1.97 1.53 1.48 ...
##  $ Perihelion.Time           : num  2458162 2457795 2458120 2457902 2457814 ...
##  $ Mean.Anomaly              : num  264.8 173.7 292.9 68.7 135.1 ...
##  $ Mean.Motion               : num  0.591 0.845 0.559 0.7 0.726 ...
##  $ Hazardous                 : chr  "True" "False" "True" "False" ...

3. Tomamos las columnas que mejor separan las clases.

Para realizar este paso vamos a utilizar la función feature_importance del algoritmo Random Forest. Esta función nos permite comparar las variables descuerdo a cuan buenas son para separa las clases. Luego tomaremos las 5 variables que mejor separa las clases.

result <- features_importance(ds_step_2, target = 'Hazardous')
## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(target)` instead of `target` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
result
## 
## Call:
##  randomForest(x = features, y = target, importance = TRUE) 
##                Type of random forest: classification
##                      Number of trees: 500
## No. of variables tried at each split: 3
## 
##         OOB estimate of  error rate: 0.34%
## Confusion matrix:
##       False True class.error
## False  3925    7 0.001780264
## True      9  746 0.011920530
plot_features_importance(result)

n_best_features = 5
# n_best_features = 15

best_features <- top_acc_features(result, top=n_best_features)
## Selecting by MeanDecreaseGini
best_features
## [1] "Minimum.Orbit.Intersection" "Absolute.Magnitude"        
## [3] "Est.Dia.in.Miles.min."      "Perihelion.Distance"       
## [5] "Inclination"
length(best_features)
## [1] 5
ds_step_3 <- ds_step_2 %>% dplyr::select(c(best_features, c(Hazardous)))
## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(best_features)` instead of `best_features` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.
rm(ds_step_2)
str(ds_step_3)
## 'data.frame':    4687 obs. of  6 variables:
##  $ Minimum.Orbit.Intersection: num  0.02528 0.18693 0.04306 0.00551 0.0348 ...
##  $ Absolute.Magnitude        : num  21.6 21.3 20.3 27.4 21.6 19.6 19.6 19.2 17.8 21.5 ...
##  $ Est.Dia.in.Miles.min.     : num  0.07905 0.09076 0.14385 0.00547 0.07905 ...
##  $ Perihelion.Distance       : num  0.808 0.718 0.951 0.984 0.968 ...
##  $ Inclination               : num  6.03 28.41 4.24 7.91 16.79 ...
##  $ Hazardous                 : chr  "True" "False" "True" "False" ...

4. Transformamos la varaible a predecir a tipo numericas

ds_step_4 <- ds_step_3 %>% 
  mutate(Hazardous = case_when(Hazardous %in% c('True') ~ 1, TRUE ~ 0))

str(ds_step_4)
## 'data.frame':    4687 obs. of  6 variables:
##  $ Minimum.Orbit.Intersection: num  0.02528 0.18693 0.04306 0.00551 0.0348 ...
##  $ Absolute.Magnitude        : num  21.6 21.3 20.3 27.4 21.6 19.6 19.6 19.2 17.8 21.5 ...
##  $ Est.Dia.in.Miles.min.     : num  0.07905 0.09076 0.14385 0.00547 0.07905 ...
##  $ Perihelion.Distance       : num  0.808 0.718 0.951 0.984 0.968 ...
##  $ Inclination               : num  6.03 28.41 4.24 7.91 16.79 ...
##  $ Hazardous                 : num  1 0 1 0 1 0 0 0 0 1 ...

5. Análisis Exploratorio

5.1. Boxplot comparativos

coparative_boxplot(feat(ds_step_4), to_col=n_best_features)

5.2. Histogramas y densidad

comparative_histplot(feat(ds_step_4), to_col=n_best_features)

5.3. Analizamos gráfico de normalidad univariado

## [[1]]
## [1] 3.7e-24
## 
## [[2]]
## [1] 3.7e-24
## 
## [[3]]
## [1] 3.7e-24
## 
## [[4]]
## [1] 3.7e-24
## 
## [[5]]
## [1] 3.7e-24

Observaciones: Al parecer solo Perihelion.Distance parece ser normal o por lo enos la mas nromal de todas.

5.3. Test de normalidad uni-variado

uni_shapiro_test(feat(ds_step_4))
## [1] "=> Variable: Minimum.Orbit.Intersection"
## [1] ""
## 
##  Shapiro-Wilk normality test
## 
## data:  features[, col_index]
## W = 0.82145, p-value < 2.2e-16
## 
## [1] "=> Variable: Absolute.Magnitude"
## [1] ""
## 
##  Shapiro-Wilk normality test
## 
## data:  features[, col_index]
## W = 0.9888, p-value < 2.2e-16
## 
## [1] "=> Variable: Est.Dia.in.Miles.min."
## [1] ""
## 
##  Shapiro-Wilk normality test
## 
## data:  features[, col_index]
## W = 0.41945, p-value < 2.2e-16
## 
## [1] "=> Variable: Perihelion.Distance"
## [1] ""
## 
##  Shapiro-Wilk normality test
## 
## data:  features[, col_index]
## W = 0.98627, p-value < 2.2e-16
## 
## [1] "=> Variable: Inclination"
## [1] ""
## 
##  Shapiro-Wilk normality test
## 
## data:  features[, col_index]
## W = 0.88555, p-value < 2.2e-16

Observaciones: En todos los casos el p-valor < 0.05 y se rechaza normalidad en todas las variables. Esto coincido con los qqplot donde en todos los casos no son normales salvo Perihelion.Distance que parece tender anormalidad.

5.4. Test de normalidad muti-variado

mult_shapiro_test(feat(ds_step_4))
## 
##  Shapiro-Wilk normality test
## 
## data:  Z
## W = 0.29729, p-value < 2.2e-16

Observaciones: El p-valore < 0.05 por lo tanto se rechaza normalidad multi-variada. Se corresponde con el resultado de los tests de shapiro uni-variados y los qqplot’s.

5.5. Test de homocedasticidad uni-variado

uni_levene_test(feat(ds_step_4), ds_step_4$Hazardous)
## [1] "=> Variable: Minimum.Orbit.Intersection"
## [1] ""
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    1  576.34 < 2.2e-16 ***
##       4685                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ""
## [1] ""
## [1] "=> Variable: Absolute.Magnitude"
## [1] ""
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    1  500.87 < 2.2e-16 ***
##       4685                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ""
## [1] ""
## [1] "=> Variable: Est.Dia.in.Miles.min."
## [1] ""
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)
## group    1  0.3586 0.5493
##       4685               
## [1] ""
## [1] ""
## [1] "=> Variable: Perihelion.Distance"
## [1] ""
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    1  16.241 5.667e-05 ***
##       4685                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ""
## [1] ""
## [1] "=> Variable: Inclination"
## [1] ""
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)  
## group    1   3.099 0.0784 .
##       4685                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] ""
## [1] ""

Observaciones

Si testeamos homocedatisidad entre cada variable y la varuabkle target encontramos que:

  • Minimum.Orbit.Intersection: p-valor < 0.05 -> Rechaza homocedasticidad.
  • Absolute.Magnitude: p-valor < 0.05 -> Rechaza homocedasticidad.
  • Est.Dia.in.Miles.min.: p-valor > 0.05 -> No Rechaza homocedasticidad.
  • Perihelion.Distance: p-valor < 0.05 -> Rechaza homocedasticidad.
  • Inclination: p-valor > 0.05 -> No Rechaza homocedasticidad.

Por lo tanto solo Est.Dia.in.Miles.min. parece tener varianza simialr con la variable target(Hazardous).

5.6. Test de homocedasticidad multi-variado

multi_boxm_test(feat(ds_step_4), ds_step_4$Hazardous)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  features
## Chi-Sq (approx.) = 3154.8, df = 15, p-value < 2.2e-16

Observaciones: El p-valor < 0.05 por lo tanto se rechaza la hipótesis nula y podemos decir que las variablesno son homocedasticas.

5.7. Correlaciones entre variables

plot_correlations(feat(ds_step_4))

5.8. Análisis completo

5.9. PCA: Comparación de variables originales con/sin la variable a predecir.

## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 4687 individuals, described by 6 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"

## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 4687 individuals, described by 5 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"

5.10. PCA: Con observaciones discriminadas pro clase. Primero quitamos

outliers para poder ver con mas claridad el biplot.

ds_without_outliers <- filter_outliers(ds_step_4, max_score=0.52)

plot_robust_pca(ds_without_outliers)

6. Train test split

c(raw_train_set, raw_test_set) %<-% train_test_split(ds_step_4, train_size=.8)
## [1] "Train Set size: 3749"
## [1] "Test set size: 938"

7. Método SMOTE para balancear el dataset.

# balanced_train_set <- smote_balance(raw_train_set, raw_train_set$Hazardous)
#rm(raw_train_set)
balanced_train_set <- raw_train_set

8. Escalamos las variables numéricas(Restamos la media y dividimos por el

desvío).

train_set <- balanced_train_set %>% 
  mutate_at(vars(-Hazardous), ~(scale(.) %>% as.vector))
test_set  <- raw_test_set %>% 
  mutate_at(vars(-Hazardous), ~(scale(.) %>% as.vector))

rm(balanced_train_set)
rm(raw_test_set)

9. Clasificacion

9.1. Entrenamos un modelo LDA

reg_formula    <- formula(Hazardous~.)
lda_model      <- lda(reg_formula, train_set)
lda_test_pred  <- predict(lda_model, test_set)

plot_cm(lda_test_pred$class, target(test_set))

graphics.off()
plot_roc(lda_test_pred$class, target(test_set))
##                                  
##  Method used: empirical          
##  ===== Positive(s) =====         
##  Number of positive(s): 157      
##  Mean of positive(s): 1.662      
##  Variance of positive(s): 0.2251 
##  ===== Negative(s) =====         
##  Number of negative(s): 781      
##  Mean of negative(s): 1.049      
##  Variance of negative(s): 0.04635
##  ===== AUC =====                 
##  Area under curve: 0.8069        
##                                  
##  =========================       
##      FPR    TPR
##  0.00000 0.0000
##  0.04866 0.6624
##  1.00000 1.0000
f_beta_score(lda_test_pred$class, target(test_set), beta=2)
## [1] "F2Score: 0.286944075672088"
lda_model$scaling
##                                    LD1
## Minimum.Orbit.Intersection -1.25346108
## Absolute.Magnitude         -1.58370375
## Est.Dia.in.Miles.min.      -0.41233546
## Perihelion.Distance         0.06937507
## Inclination                -0.01813808

9.2. Entrenamos un modelo QDA

qda_model      <- qda(reg_formula, train_set)
qda_test_pred  <- predict(qda_model, test_set)

plot_cm(qda_test_pred$class, target(test_set))

plot_roc(qda_test_pred$class, target(test_set))

##                                   
##  Method used: empirical           
##  ===== Positive(s) =====          
##  Number of positive(s): 157       
##  Mean of positive(s): 1.93        
##  Variance of positive(s): 0.06557 
##  ===== Negative(s) =====          
##  Number of negative(s): 781       
##  Mean of negative(s): 1.003       
##  Variance of negative(s): 0.002558
##  ===== AUC =====                  
##  Area under curve: 0.9637         
##                                   
##  =========================        
##       FPR    TPR
##  0.000000 0.0000
##  0.002561 0.9299
##  1.000000 1.0000
f_beta_score(qda_test_pred$class, target(test_set), beta=2)
## [1] "F2Score: 0.0676674327386125"

9.3. Entrenamos un modelo RDA

rda_model      <- rda(reg_formula, train_set)
rda_test_pred  <- predict(rda_model, test_set)

plot_cm(rda_test_pred$class, target(test_set))

plot_roc(rda_test_pred$class, target(test_set))

##                                   
##  Method used: empirical           
##  ===== Positive(s) =====          
##  Number of positive(s): 157       
##  Mean of positive(s): 1.93        
##  Variance of positive(s): 0.06557 
##  ===== Negative(s) =====          
##  Number of negative(s): 781       
##  Mean of negative(s): 1.003       
##  Variance of negative(s): 0.002558
##  ===== AUC =====                  
##  Area under curve: 0.9637         
##                                   
##  =========================        
##       FPR    TPR
##  0.000000 0.0000
##  0.002561 0.9299
##  1.000000 1.0000
f_beta_score(rda_test_pred$class, target(test_set), beta=2)
## [1] "F2Score: 0.0676674327386125"

9.4. Entrenamos un modelo de regresión logística

rl_model     <- glm(reg_formula, train_set, family=binomial)
rl_test_pred <- predict(rl_model, test_set)

rl_threshold <- 0.4
rl_test_pred_threshold <- ifelse(rl_test_pred >= rl_threshold, 1, 0)

plot_cm(rl_test_pred_threshold, target(test_set))

plot_roc(rl_test_pred_threshold, target(test_set))

##                                  
##  Method used: empirical          
##  ===== Positive(s) =====         
##  Number of positive(s): 157      
##  Mean of positive(s): 0.7389     
##  Variance of positive(s): 0.1942 
##  ===== Negative(s) =====         
##  Number of negative(s): 781      
##  Mean of negative(s): 0.02177    
##  Variance of negative(s): 0.02132
##  ===== AUC =====                 
##  Area under curve: 0.8585        
##                                  
##  =========================       
##      FPR    TPR
##  0.00000 0.0000
##  0.02177 0.7389
##  1.00000 1.0000
f_beta_score(rl_test_pred_threshold, target(test_set), beta=2)
## [1] "F2Score: 0.76215505913272"

9.5. Entrenamos un modelo SVM

svm_model <- svm(reg_formula, train_set, kernel="radial")

svm_test_pred <- predict(svm_model, test_set)
svm_threshold <- 0.5
svm_test_pred_threshold <- ifelse(svm_test_pred >= rl_threshold, 1, 0)

plot_text_cm(svm_test_pred_threshold, target(test_set))
##        Prediction
## Reality   0   1
##       0 760  23
##       1  21 134
plot_roc(svm_test_pred_threshold, target(test_set))

##                                 
##  Method used: empirical         
##  ===== Positive(s) =====        
##  Number of positive(s): 157     
##  Mean of positive(s): 0.8535    
##  Variance of positive(s): 0.1258
##  ===== Negative(s) =====        
##  Number of negative(s): 781     
##  Mean of negative(s): 0.02689   
##  Variance of negative(s): 0.0262
##  ===== AUC =====                
##  Area under curve: 0.9133       
##                                 
##  =========================      
##      FPR    TPR
##  0.00000 0.0000
##  0.02689 0.8535
##  1.00000 1.0000
f_beta_score(svm_test_pred_threshold, target(test_set), beta=2)
## [1] "F2Score: 0.855683269476373"

9.6. Entrenamos un modelo XGBoost

xgboost_model <- xgboost(
 as.matrix(feat(train_set)), 
 target(train_set),
 eta = 0.1,
 max_depth = 10, 
 nround=5000, 
 objective = "binary:logistic",
 nthread = 24
)
## [01:02:06] WARNING: amalgamation/../src/learner.cc:1095: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.
## [1]  train-logloss:0.599057 
## [2]  train-logloss:0.521974 
## [3]  train-logloss:0.457647 
## [4]  train-logloss:0.403239 
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xgb_test_pred <- predict(xgboost_model, as.matrix(feat(test_set)))
xgb_threshold <- 0.5
xgb_test_pred_threshold <- ifelse(xgb_test_pred >= xgb_threshold, 1, 0)

plot_cm(xgb_test_pred_threshold, target(test_set))

plot_roc(xgb_test_pred_threshold, target(test_set))

##                                  
##  Method used: empirical          
##  ===== Positive(s) =====         
##  Number of positive(s): 157      
##  Mean of positive(s): 0.9682     
##  Variance of positive(s): 0.03103
##  ===== Negative(s) =====         
##  Number of negative(s): 781      
##  Mean of negative(s): 0          
##  Variance of negative(s): 0      
##  ===== AUC =====                 
##  Area under curve: 0.9841        
##                                  
##  =========================       
##  FPR    TPR
##    0 0.0000
##    0 0.9682
##    1 1.0000
f_beta_score(xgb_test_pred_threshold, target(test_set), beta=2)
## [1] "F2Score: 0.974358974358974"

10. KMeans Clustering

10.1. Primero definimos cuantos grupos utilizar.

Típica con estimadores de la normal.

scaled_data_1 <- feat(ds_step_4) %>% mutate(~(scale(.) %>% as.vector))

Escalamiento diferente de la tipica normal.

scaled_data_2 <- apply(
  feat(ds_step_4), 
  2, 
  function(x) { (x - min(x)) / (max(x) - min(x))}
)
clustering_metrics_plot(scaled_data_1)

clustering_metrics_plot(scaled_data_2)

10.2. Kmeans

n_clusters <- 2
kmeans_model <- kmeans(scaled_data_1, n_clusters)

km_ds_step_4 <- data.frame(ds_step_4)
km_ds_step_4$kmeans <- kmeans_model$cluster

10.2. biplot

ds_without_outliers <- filter_outliers(km_ds_step_4, max_score=0.5)

plot_robust_pca(
  ds_without_outliers %>% dplyr::select(-kmeans),
  groups = factor(ds_without_outliers$kmeans),
)

10.3 Hierarchical Clustering

Matriz de distancias euclídeas

mat_dist <- dist(x = ds_step_4, method = "euclidean") 

Dendrogramas (según el tipo de segmentación jerárquica aplicada)

hc_complete <- hclust(d = mat_dist, method = "complete") 
hc_average  <- hclust(d = mat_dist, method = "average")
hc_single   <- hclust(d = mat_dist, method = "single")
hc_ward     <- hclust(d = mat_dist, method = "ward.D2")

Calculo del coeficiente de correlación cofenetico

cor(x = mat_dist, cophenetic(hc_complete))
## [1] 0.8024213
cor(x = mat_dist, cophenetic(hc_average))
## [1] 0.8064622
cor(x = mat_dist, cophenetic(hc_single))
## [1] 0.5078482
cor(x = mat_dist, cophenetic(hc_ward))
## [1] 0.5889577

Construcción de un dendograma usando los resultados de la técnica de Ward

n_clusters <- 2

graphics.off()
plot(hc_ward )
rect.hclust(hc_ward, k=n_clusters, border="red")
hc_ds <- data.frame(ds_step_4)
hc_ds$her_ward <- cutree(hc_ward, k=n_clusters)
ds_without_outliers <- filter_outliers(hc_ds, max_score=0.57)

plot_robust_pca(
  ds_without_outliers %>% dplyr::select(-her_ward),
  groups = factor(ds_without_outliers$her_ward),
  colours=c("orange","cyan","blue","magenta","yellow","black"),
  labels=c("grupo 1", "grupo 2","grupo 3","grupo 4","grupo 5","grupo 6")
)

plot_robust_pca(ds_without_outliers)

 

Realizado por Adrian Marino

adrianmarino@gmail.com